Fermionic Topological Order on Generic Triangulations

Topological Effects on Minimum Weight Steiner Triangulations

We are concerned with a long-standing classical problem in computational geometry: that of finding a minimum weight triangulation of a point set. A minimum weight triangulation is a triangulation which minimizes the sum of the Euclidean lengths of the edges used. Triangulations are very useful objects in the realm of applied computational geometry. By allowing for decompositions of space into s...

On Order-generic Queries

We consider relational databases organized over an ordered domain with some additional relations|a typical example is the ordered domain of rational numbers together with the ternary relation + of addition. In the focus of our study are the rst order queries that are invariant under order-preserving \permutations"|such queries are called order-generic. In fact, we consider two formalizations of...

Higher Order Delaunay Triangulations

Fermionic Symmetry Protected Topological Phases and Cobordisms

It has been proposed recently that interacting Symmetry Protected Topological Phases can be classified using cobordism theory. We test this proposal in the case of Fermionic SPT phases with Z2 symmetry, where Z2 is either time-reversal or an internal symmetry. We find that cobordism classification correctly describes all known Fermionic SPT phases in space dimensionD ≤ 3 and also predicts that ...

Fermionic Coset Models as Topological Models

By considering the fermionic realization of G/H coset models, we show that the partition function for the U(1)/U(1) model defines a Topological Quantum Field Theory and coincides with that for a 2dimensional Abelian BF system. In the non-Abelian case, we prove the topological character of G/G coset models by explicit computation, also finding a natural extension of 2-dimensional BF systems with...